Operations on Functions

Front

What is the definition of function multiplication?

Back

Function multiplication, denoted as (fg)(x), is the product of two functions f(x) and g(x), calculated as f(x) * g(x).

Front

Given f(x) = x^2 + 4 and g(x) = x^3 - 4, find (fg)(x).

Back

(fg)(x) = x^5 + 4x^3 - 4x^2 - 16.

Front

What is the definition of function subtraction?

Back

Function subtraction, denoted as (f - g)(x), is the difference between two functions f(x) and g(x), calculated as f(x) - g(x).

Front

Given f(x) = 3x^2 + 7x and g(x) = 2x^2 - x - 1, find (f - g)(x).

Back

(f - g)(x) = x^2 + 8x + 1.

Front

What is the definition of function division?

Back

Function division, denoted as (f/g)(x), is the quotient of two functions f(x) and g(x), calculated as f(x) / g(x), provided g(x) ≠ 0.

Front

Given f(x) = x + 2 and g(x) = x^2 - 4, find (f/g)(x).

Back

(f/g)(x) = 1/(x - 2).

Front

What is the definition of function composition?

Back

Function composition, denoted as (f ∘ g)(x), is the application of one function to the results of another function, calculated as f(g(x)).

Front

Given f(x) = x^2 - 2x + 1 and g(x) = x - 1, find (f/g)(x).

Back

(f/g)(x) = (x - 1).

Front

What is the definition of a polynomial function?

Back

A polynomial function is a function that can be expressed in the form f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n, a_(n-1), ..., a_0 are constants and n is a non-negative integer.

Front

Given g(x) = 6x + 4 and f(x) = 2x - 7, find (fg)(x).

Back

(fg)(x) = 12x^2 - 34x - 28.